Abstract

This simulation study investigated the recovery item and person parameters of three-parameter logistic and multiple-choice models for mathematics testing in selected-response format test. A potential problem with such the study is the accuracy of simultaneous estimation of item and person parameters in item response theory.
Item responses were simulated using three-parameter logistic and multiple-choice models. Samples of 400, 1000, and 3000 simulated examinees and tests lengths of 20, 40, and 60 were generated. The response patterns according to models was run in PARSCALE. The root mean squared error between recovered and actual item characteristic curves served as the principal measure of estimation accuracy for items. The data were analyzed using the fixed effect MANOVA on RMSE ability, RMSE item parameters estimate to identify the significant main effects.
The result of the study indicate that the differences of the perfomance between three-parameter logistic and multiple-choice models on the format test analysis in mathematics subject are significant at the level of  = .05. Each model which generated ability estimation and item parameter is significantly different. Multiple-choice model provided higher accurate estimation than three-parameter logistic model. In addition, the test information given by multiple-choice model is three times higher than three-parameter logistic model although it could not offer a solid conclusion related to the sample size on each test length which gives the optimal score of test information.
Key words: parameter recovery, mathematics testing, simulation study